Complete for Example 4.16. The command syms constructs symbolic objects, in this case a and A. The command det operating on a symbolic matrix does symbolic calculations. Notice that it computed the...

Complete

for

Example 4.16. The command syms constructs symbolic objects, in this case a and A. The command det operating on a symbolic matrix does symbolic calculations. Notice that it computed the same determinant that was found in Example 4.15. The command solve finds the solutions to det(A) = 0. After assigning a = -8, the first of the two values, to locations (2,1) and (3,3), the command null(A) finds the null space of the matrix A. The result is that the null space is spanned by precisely

the result of Example 4.15. The command colspace(A) finds a basis for the column space of A. There are two vectors, so the rank of A is 2.

To finish this section, we present an old

method of solving a system of

equations in

unknowns called Cramer’s rule. It is useful for solving

and

systems, but otherwise is too computationally expensive to use for larger systems. It does have theoretical uses in areas of mathematics such as differential equations.